An average American household uses about 1.04×104 kWh (kilowatt hours) of electricity a year. If a power station generates 2.496×1010 kWh per year, how many households can it serve? Write your answer in scientific notation, expressed to the exact decimal place

Answer 1

To find out how many households a power station can serve, we can divide the total electricity generated by the power station by the electricity used by an average household.

Given:

• Total electricity generated by the power station: \(2.496 \times 10^{10}\) kWh
• Electricity used by an average household: \(1.04 \times 10^{4}\) kWh per year

We can calculate the number of households served as follows:

\[ \text{Number of households} = \frac{\text{Total electricity generated}}{\text{Electricity used by one household}} = \frac{2.496 \times 10^{10}}{1.04 \times 10^{4}} \]

To perform this division, we can simplify it as follows:

\[ \frac{2.496}{1.04} \times \frac{10^{10}}{10^{4}} = \frac{2.496}{1.04} \times 10^{10 - 4} = \frac{2.496}{1.04} \times 10^{6} \]

Now, we compute \(\frac{2.496}{1.04}\):

\[ \frac{2.496}{1.04} \approx 2.4 \]

This gives us:

\[ \text{Number of households} \approx 2.4 \times 10^{6} \]

Therefore, the power station can serve approximately \(2.4 \times 10^{6}\) households.

Answer 2

There are about 1.6×103 meters in a mile. About how many miles are there in 3.52×107 meters? Write your answer in scientific notation, expressed to the exact decimal place

Answer 3

To find out how many miles are in \(3.52 \times 10^7\) meters, we can divide the total number of meters by the number of meters in a mile.

Given:

• Meters in a mile: \(1.6 \times 10^3\) meters
• Total meters: \(3.52 \times 10^7\) meters

We will calculate the number of miles as follows:

\[ \text{Number of miles} = \frac{\text{Total meters}}{\text{Meters in a mile}} = \frac{3.52 \times 10^7}{1.6 \times 10^3} \]

We can simplify this fraction:

\[ \frac{3.52}{1.6} \times \frac{10^7}{10^3} = \frac{3.52}{1.6} \times 10^{7 - 3} = \frac{3.52}{1.6} \times 10^4 \]

Now we compute \(\frac{3.52}{1.6}\):

\[ \frac{3.52}{1.6} = 2.2 \]

Putting it all together:

\[ \text{Number of miles} = 2.2 \times 10^4 \]

Thus, there are approximately \(2.2 \times 10^4\) miles in \(3.52 \times 10^7\) meters.

Answer 4

An online data storage facility has 1.326×1013 bytes of storage available. It has 2.6×104 customers. How many bytes of storage can each customer use? Write your answer in scientific notation, expressed to the exact decimal place

Answer 5

To determine how many bytes of storage each customer can use, we need to divide the total number of bytes of storage available by the number of customers.

Given:

• Total bytes of storage: \(1.326 \times 10^{13}\) bytes
• Number of customers: \(2.6 \times 10^{4}\)

We calculate the storage per customer as follows:

\[ \text{Storage per customer} = \frac{\text{Total bytes of storage}}{\text{Number of customers}} = \frac{1.326 \times 10^{13}}{2.6 \times 10^{4}} \]

We can simplify this fraction:

\[ \text{Storage per customer} = \frac{1.326}{2.6} \times \frac{10^{13}}{10^{4}} = \frac{1.326}{2.6} \times 10^{13 - 4} = \frac{1.326}{2.6} \times 10^{9} \]

Now we compute \(\frac{1.326}{2.6}\):

\[ \frac{1.326}{2.6} \approx 0.51 \]

Putting it all together:

\[ \text{Storage per customer} \approx 0.51 \times 10^{9} \]

To express this in correct scientific notation, we can adjust \(0.51\) to \(5.1\) and decrease the exponent by 1:

\[ 0.51 \times 10^{9} = 5.1 \times 10^{8} \]

Thus, each customer can use approximately \(5.1 \times 10^{8}\) bytes of storage.

Answer 6

A public aquarium is being built to contain neon tetras. Each neon tetra needs 1.25 gallons of water. The aquarium will contain 1×105 gallons of water. How many tetras can it house? Write the answer in scientific notation

Answer 7

To determine how many neon tetras the aquarium can house, we need to divide the total amount of water in gallons by the amount of water each neon tetra requires.

Given:

• Water needed per neon tetra: \(1.25\) gallons
• Total water in the aquarium: \(1 \times 10^5\) gallons

We can calculate the number of neon tetras as follows:

\[ \text{Number of tetras} = \frac{\text{Total water}}{\text{Water needed per tetra}} = \frac{1 \times 10^5 \text{ gallons}}{1.25 \text{ gallons/tetra}} \]

Now we simplify the expression:

\[ \text{Number of tetras} = \frac{1 \times 10^5}{1.25} \]

Calculating the division:

\[ \frac{1}{1.25} = 0.8 \]

Now, substituting back into our expression:

\[ \text{Number of tetras} = 0.8 \times 10^5 \]

To express this in scientific notation, we can convert \(0.8\) to \(8\) and decrease the exponent by 1:

\[ 0.8 \times 10^5 = 8.0 \times 10^{4} \]

Thus, the aquarium can house approximately \(8.0 \times 10^{4}\) neon tetras.

Answer 8

A feather weighs 0.0082 g. How many feathers would you need to make a weight of 4.1×103 g? Write the answer in scientific notation

Answer 9

To determine how many feathers are needed to make a weight of \(4.1 \times 10^3\) grams when each feather weighs \(0.0082\) grams, we can use the formula:

\[ \text{Number of feathers} = \frac{\text{Total weight}}{\text{Weight of one feather}} \]

Substituting in the values:

\[ \text{Number of feathers} = \frac{4.1 \times 10^3 \text{ g}}{0.0082 \text{ g}} \]

Now, we can perform the division:

1. First, calculate \( \frac{4.1}{0.0082} \): \[ \frac{4.1}{0.0082} \approx 500 \]

2. Then, account for the scientific notation: \[ \frac{10^3}{1} = 10^{3} \]

Putting it all together, we get:

\[ \text{Number of feathers} \approx 500 \times 10^{3} = 5.0 \times 10^{5} \]

Thus, the total number of feathers needed is approximately \(5.0 \times 10^{5}\) feathers.

Answer 10

A rectangular park has an area of 1.36×108 ft2 . The length of the park is 1.6×104 ft. Divide the area by the length to find the width of the park.

Answer 11

To find the width of the rectangular park, we can divide the area of the park by its length.

Given:

• Area of the park: \(1.36 \times 10^8\) ft²
• Length of the park: \(1.6 \times 10^4\) ft

We will calculate the width using the formula:

\[ \text{Width} = \frac{\text{Area}}{\text{Length}} = \frac{1.36 \times 10^8, \text{ft}^2}{1.6 \times 10^4, \text{ft}} \]

This can be simplified as follows:

\[ \text{Width} = \frac{1.36}{1.6} \times \frac{10^8}{10^4} = \frac{1.36}{1.6} \times 10^{8 - 4} = \frac{1.36}{1.6} \times 10^4 \]

Now, we compute \( \frac{1.36}{1.6} \):

\[ \frac{1.36}{1.6} = 0.85 \]

Putting it all together, we have:

\[ \text{Width} = 0.85 \times 10^4 \]

To express this in scientific notation, we can convert \(0.85\) to \(8.5\) and decrease the exponent by 1:

\[ 0.85 \times 10^4 = 8.5 \times 10^3 \]

Thus, the width of the park is \(8.5 \times 10^3\) ft.

Answer 12

Divide 3.3×10^4 by 5.5×10^7

Answer 13

To divide \(3.3 \times 10^4\) by \(5.5 \times 10^7\), we can separately divide the coefficients and the powers of ten.

The division can be expressed as:

\[ \frac{3.3 \times 10^4}{5.5 \times 10^7} = \frac{3.3}{5.5} \times \frac{10^4}{10^7} \]

1. Dividing the coefficients: \[ \frac{3.3}{5.5} = 0.6 \]

2. Dividing the powers of ten: \[ \frac{10^4}{10^7} = 10^{4 - 7} = 10^{-3} \]

Now, combine the results:

\[ 0.6 \times 10^{-3} \]

To express this in scientific notation, we can convert \(0.6\) to \(6\) and decrease the exponent by 1:

\[ 0.6 \times 10^{-3} = 6.0 \times 10^{-4} \]

Thus, the result of \( \frac{3.3 \times 10^4}{5.5 \times 10^7} \) is

\[ 6.0 \times 10^{-4} \]

Answer 14

A city lunch program for seniors received a grant of 1.925×106 dollars. Divide that figure by the cost of $2.75 per lunch to find out how many senior lunches the grant can provide. Write the answer in scientific notation

Answer 15

To determine how many senior lunches the grant can provide, we'll divide the total grant amount by the cost per lunch.

Given:

• Total grant amount: \(1.925 \times 10^{6}\) dollars
• Cost per lunch: \(2.75\) dollars

We can calculate the number of lunches as follows:

\[ \text{Number of lunches} = \frac{\text{Total grant amount}}{\text{Cost per lunch}} = \frac{1.925 \times 10^{6}}{2.75} \]

First, we will calculate \(\frac{1.925}{2.75}\):

\[ \frac{1.925}{2.75} \approx 0.7 \]

Next, we need to account for the scientific notation. Since \(2.75\) does not have a power of ten, it remains as is:

\[ \text{Number of lunches} \approx 0.7 \times 10^{6} \]

To express this in proper scientific notation, we can convert \(0.7\) to \(7\) and decrease the exponent by 1:

\[ 0.7 \times 10^{6} = 7.0 \times 10^{5} \]

Thus, the number of senior lunches that the grant can provide is approximately

\[ \boxed{7.0 \times 10^{5}} \] lunches.

Answer 16

Solomon needs to distribute 10.5 gallons of perfume among 3.5×102 containers. How many gallons of perfume will be in each container? Write the answer in scientific notation

Answer 17

To find out how many gallons of perfume will be in each container, we need to divide the total gallons of perfume by the number of containers.

Given:

• Total gallons of perfume: \(10.5\) gallons
• Number of containers: \(3.5 \times 10^2\)

Using the formula for the amount of perfume per container:

\[ \text{Gallons per container} = \frac{\text{Total gallons}}{\text{Number of containers}} = \frac{10.5}{3.5 \times 10^2} \]

We can simplify this division as follows:

\[ \text{Gallons per container} = \frac{10.5}{3.5} \cdot \frac{1}{10^2} \]

First, calculate \(\frac{10.5}{3.5}\):

\[ \frac{10.5}{3.5} = 3 \]

Now we substitute this back into the equation:

\[ \text{Gallons per container} = 3 \cdot \frac{1}{10^2} = 3 \cdot 10^{-2} \]

Then, express this in scientific notation:

\[ 3 \cdot 10^{-2} = 3.0 \times 10^{-2} \]

Thus, the gallons of perfume in each container is

\[ \boxed{3.0 \times 10^{-2}} \text{ gallons.} \]

Answer 18

A large pavilion is made of 2.967×105 bricks. There are 6.9 bricks per square foot. How many square feet is the pavilion? Write the answer in scientific notation

Answer 19

To find out how many square feet the pavilion covers, we need to divide the total number of bricks by the number of bricks per square foot.

Given:

• Total number of bricks: \(2.967 \times 10^5\) bricks
• Number of bricks per square foot: \(6.9\) bricks/sq ft

The formula for the area in square feet is:

\[ \text{Area (sq ft)} = \frac{\text{Total bricks}}{\text{Bricks per square foot}} \]

Substituting the values:

\[ \text{Area} = \frac{2.967 \times 10^5}{6.9} \]

Now, calculate the division:

1. First, calculate \( \frac{2.967}{6.9} \):

\[ \frac{2.967}{6.9} \approx 0.430

\]

2. Now, we incorporate the power of ten:

\[ \text{Area} = 0.430 \times 10^5 \]

To express this in proper scientific notation, we adjust \(0.430\) to \(4.30\) and decrease the exponent by 1:

\[ 0.430 \times 10^5 = 4.30 \times 10^4 \]

Thus, the area of the pavilion is approximately

\[ \boxed{4.30 \times 10^{4}} \text{ square feet.} \]